Axioms, Volume 14, Issue 1

Deep learning methods using neural networks for solving partial differential equations (PDEs) have emerged as a new paradigm. However, many of these methods approximate solutions by optimizing loss functions, often encountering convergence issues and...

In this paper, we use the averaging method to find an approximate solution for the optimal control of parabolic differential inclusion with fast-oscillating coefficients on a semi-axis.

This work aims to provide approximate solutions for singularly perturbed problems with periodic boundary conditions using quintic B-splines and collocation. The well-known Shishkin mesh strategy is applied for mesh construction. Convergence analysis...

This research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research als...

Additive manufacturing technologies have allowed the production of complex geometries that are typically obtained by applying topology optimization techniques. The outcome of the optimization process is a tessellated geometry, which has reduced aesth...

In this paper, we introduce a quantum private comparison (QPC) protocol designed for two players to securely and privately assess the equality of their private information. The protocol utilizes four-particle cluster states prepared by a semi-honest...

We examine the qualitative properties of ionic flows through membrane channels via Poisson–Nernst–Planck (PNP) type models with steric effects under relaxed electroneutrality boundary conditions, and more realistic setups in the study of...

A problem that geometers have always been concerned with is when a closed manifold is isometric to a round sphere. A classical result shows that a closed locally conformally flat Einstein manifold is always isometric to a quotient of a round sphere....

This paper considers the Horn’s hypergeometric function H3, which is closely related to other hypergeometric functions and has various mathematical or physical applications. The problem of analytical extension of this function is solved using a...

We elaborate on the brane configuration that gives rise to a QCD-like gauge theory that confines at low energies and becomes scale invariant at the highest energies. In the limit where the rank of the gauge group is large, a gravitational description...